Robust Design-Based Estimation and Inference for Stratified Randomized Trials with Varying Cluster Sizes
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群组规模不等的分层随机试验：稳健设计估计与推断
- 研究问题
- 论文研究群组规模不同的分层随机试验中，逐层处理对照均值差的平均为何可能偏离样本平均处理效应，以及如何稳健估计推断。
- 方法与思路
- 作者分析群组规模与效应的协方差导致的权重偏差，采用先汇总组内结果的 Hájek 比率估计，并构造设计方差和改进检验。
- 材料陈述的贡献
- 摘要称刻画常数量级偏差，证明替代估计在两类试验扩张方式下相合，并提出渐近保守方差估计及适用于中等群组数的检验。
- 阅读关注点
- 应核对样本平均效应的加权定义、两类渐近序列、单处理或单对照层的方差构造，以及协变量调整所需的方差正交性质。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收；摘要未列出相合性与保守性条件，也未给出改进检验的具体形式。
原文摘要
Clustered randomized controlled trials are often stratified or pair-matched to improve covariate balance and efficiency. Sample average treatment effects (SATEs) are commonly estimated by averaging stratum-level treatment-control mean contrasts -- an approach that is natural and widely used. We show that, in stratified clustered trials with heterogeneous cluster sizes, such estimators need not be consistent for the SATE. They can converge to the wrong limit even under correct randomization and without model misspecification. The source is a covariance between cluster sizes and treatment effects: stratumwise averaging mis-weights clusters in a way that produces bias of constant order, regardless of sample size. We study the Hájek (ratio) estimator as a robust alternative. By aggregating outcomes within treatment groups before taking their difference, it remains consistent in clustered trials that grow by increasing strata sizes or the number of strata. Despite that, its use in design-based analyses of clustered trials has been limited by the lack of variance estimators. We develop a design-based variance estimator that applies to any number of strata of any size, and show that it is asymptotically conservative, a property that holds even when some strata contain only a single treated or control unit. We also present tests improving the coverage of Wald tests when the number of clusters is moderate. The framework extends naturally to covariate-adjusted estimators via a variance orthogonality property.